Logic of Non-monotonic Interactive Proofs

  • Simon Kramer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7750)


We propose a monotonic logic of internalised non-monotonic or instant interactive proofs (LiiP) and reconstruct an existing monotonic logic of internalised monotonic or persistent interactive proofs (LiP) as a minimal conservative extension of LiiP. Instant interactive proofs effect a fragile epistemic impact in their intended communities of peer reviewers that consists in the impermanent induction of the knowledge of their proof goal by means of the knowledge of the proof with the interpreting reviewer: If my peer reviewer knew my proof then she would at least then know that its proof goal is true. Their impact is fragile and their induction of knowledge impermanent in the sense of being the case possibly only at the instant of learning the proof. This accounts for the important possibility of internalising proofs of statements whose truth value can vary, which, as opposed to invariant statements, cannot have persistent proofs. So instant interactive proofs effect a temporary transfer of certain propositional knowledge (knowable ephemeral facts) via the transmission of certain individual knowledge (knowable non-monotonic proofs) in distributed systems of multiple interacting agents.


agents as proof- and signature-checkers constructive Kripke-semantics interpreted communication multi-agent distributed systems interactive and oracle computation proofs as sufficient evidence 


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  1. 1.
    Kramer, S.: Logic of non-monotonic interactive proofs (formal theory of temporary knowledge transfer). Technical Report 1208.1842, arXiv (2012),
  2. 2.
    Kramer, S.: A logic of interactive proofs (formal theory of knowledge transfer). Technical Report 1201.3667, arXiv (2012),
  3. 3.
    Makinson, D.: How To Go Nonmonotonic. In: Handbook of Philosophical Logic, 2nd edn., vol. 12. Springer (2005)Google Scholar
  4. 4.
    Meyer, J.J., Veltman, F.: Intelligent Agents and Common Sense Reasoning. In: [5]Google Scholar
  5. 5.
    Blackburn, P., van Benthem, J., Wolter, F. (eds.): Handbook of Modal Logic. Studies in Logic and Practical Reasoning, vol. 3. Elsevier (2007)Google Scholar
  6. 6.
    Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning about Knowledge. MIT Press (1995)Google Scholar
  7. 7.
    Hendricks, V., Roy, O. (eds.): Epistemic Logic: 5 Questions. Automatic Press (2010)Google Scholar
  8. 8.
    Katz, J.: Digital Signatures. Springer (2010)Google Scholar
  9. 9.
    Anderson, R.: Security Engineering: A Guide to Building Dependable Distributed Systems, 2nd edn. Wiley (2008)Google Scholar
  10. 10.
    Artemov, S.: The logic of justifications. The Review of Symbolic Logic 1(4) (2008)Google Scholar
  11. 11.
    Hindley, J., Seldin, J.: Lambda-Calculus and Combinators, 2nd edn. Cambridge University Press (2008)Google Scholar
  12. 12.
    Baltag, A., Renne, B., Smets, S.: The Logic of Justified Belief Change, Soft Evidence and Defeasible Knowledge. In: Ong, L., de Queiroz, R. (eds.) WoLLIC 2012. LNCS, vol. 7456, pp. 168–190. Springer, Heidelberg (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Simon Kramer
    • 1
  1. 1.University of LuxembourgLuxembourg

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